Blender Game renders the scene wrong
Some faces won't render so what it means is that you propably have Backface culling activated(means that only the faces in the direction of the normals are getting rendered).

Select the object whose faces won't appear. 

Then go into edit mode by pressing tab.

In the "N" panel find the mesh display and under "Normals" select faces (the 3rd icon).

Blue lines (these segments are called Normals) are gonna come out of the faces of your object. The faces will be rendered from the side these blue lines go to. So if the faces that won't render have their blue lines going inside, it means this is your problem.

What you should do to fix this is:

press ctrl+N (with the faces still selected) and then in the "T" panel the "Make normals consistent" option is gonna appear with an unchecked box. Check it and it should be fine. This is the manual way in case of selecting all faces and pressing ctrl+N won't fix your problem.

p.s. if you want your plane to render both ways, deactivate backface culling in the "N" panel below shading mode.